Analogy and Structure provides the necessary foundation for understanding the nature of analogical and structuralist (or rule-based) approaches to describing behavior. In the first part of this book, the mathematical properties of rule approaches are developed; in the second part, the analogical alternative to rules is developed. This book serves as the mathematical basis for Analogical Modeling of Language (Kluwer, 1989). Features include: A Natural Measure of Uncertainty: The disagreement between randomly chosen occurences avids the difficulties of using entropy as the measure of uncertainty. Optimal Descriptions: The implicit assumption of structuralist descriptions (namely, that descriptions of behavior should be corrected and minimal) can be derived from more fundamental statements about the uncertainty of rule systems. Problems with Rule Approaches: The correct description of nondeterministic behavior leads to an atomistic, analog alternative to structuralist (or rule-based) descriptions. Natural Statistics: Traditional statistical tests are eliminated in favor of statistically equivalent decision rules that involve little or no mathematical calculation. Psycholinguistic Factors: Analogical models, unlike, neural networks, directly account for probabilistic learning as well as reaction times in world-recognition experiments.

1. Structuralist Versus Analogical Descriptions ONE important purpose of this book is to compare two completely dif ferent approaches to describing language. The first of these approaches, commonly called stnlctllralist, is the traditional method for describing behavior. Its methods are found in many diverse fields - from biological taxonomy to literary criticism. A structuralist description can be broadly characterized as a system of classification. The fundamental question that a structuralist description attempts to answer is how a general contextual space should be partitioned. For each context in the partition, a rule is defined. The rule either specifies the behavior of that context or (as in a taxonomy) assigns a name to that context. Structuralists have implicitly assumed that descriptions of behavior should not only be correct, but should also minimize the number of rules and permit only the simplest possible contextual specifications. It turns out that these intuitive notions can actually be derived from more fundamental statements about the uncertainty of rule systems. Traditionally, linguistic analyses have been based on the idea that a language is a system of rules. Saussure, of course, is well known as an early proponent of linguistic structuralism, as exemplified by his characterization of language as "a self-contained whole and principle of classification" (Saussure 1966:9). Yet linguistic structuralism did not originate with Saussure - nor did it end with "American structuralism.""

1. Structuralist Versus Analogical Descriptions ONE important purpose of this book is to compare two completely dif ferent approaches to describing language. The first of these approaches, commonly called stnlctllralist, is the traditional method for describing behavior. Its methods are found in many diverse fields - from biological taxonomy to literary criticism. A structuralist description can be broadly characterized as a system of classification. The fundamental question that a structuralist description attempts to answer is how a general contextual space should be partitioned. For each context in the partition, a rule is defined. The rule either specifies the behavior of that context or (as in a taxonomy) assigns a name to that context. Structuralists have implicitly assumed that descriptions of behavior should not only be correct, but should also minimize the number of rules and permit only the simplest possible contextual specifications. It turns out that these intuitive notions can actually be derived from more fundamental statements about the uncertainty of rule systems. Traditionally, linguistic analyses have been based on the idea that a language is a system of rules. Saussure, of course, is well known as an early proponent of linguistic structuralism, as exemplified by his characterization of language as "a self-contained whole and principle of classification" (Saussure 1966:9). Yet linguistic structuralism did not originate with Saussure - nor did it end with "American structuralism.""

Analogy and Structure provides the necessary foundation for understanding the nature of analogical and structuralist (or rule-based) approaches to describing behavior. In the first part of this book, the mathematical properties of rule approaches are developed; in the second part, the analogical alternative to rules is developed. This book serves as the mathematical basis for Analogical Modeling of Language (Kluwer, 1989). Features include: A Natural Measure of Uncertainty: The disagreement between randomly chosen occurences avids the difficulties of using entropy as the measure of uncertainty. Optimal Descriptions: The implicit assumption of structuralist descriptions (namely, that descriptions of behavior should be corrected and minimal) can be derived from more fundamental statements about the uncertainty of rule systems. Problems with Rule Approaches: The correct description of nondeterministic behavior leads to an atomistic, analog alternative to structuralist (or rule-based) descriptions. Natural Statistics: Traditional statistical tests are eliminated in favor of statistically equivalent decision rules that involve little or no mathematical calculation. Psycholinguistic Factors: Analogical models, unlike, neural networks, directly account for probabilistic learning as well as reaction times in world-recognition experiments.